MATH207 Vector Calculus
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| Course Code | Course Title | Weekly Hours* | ECTS | Weekly Class Schedule | ||||||
| T | P | |||||||||
| MATH207 | Vector Calculus | 3 | 3 | 6 | ||||||
| Prerequisite | MATH101 | It is a prerequisite to | None |
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| Lecturer | Seyednima Rabiei | Office Hours / Room / Phone | Tuesday: 14:00-16:00 Thursday: 11:00-13:00 Friday: 12:00-14:00 |
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| nrabiei@ius.edu.ba | ||||||||||
| Assistant | Nima Rabiei | Assistant E-mail | ||||||||
| Course Objectives | This course is intended to cover mulit-variable and vector calculus which are useful Mathematical methods and tools to engineering students that are related to solving practical problems . Topics include vector, multi-variable functions, partial derivatives, double and triple integral, polar, cylindrical and spherical coordinates, integration on line and surfaces. After completing this course, students should be able to: 1. Understand the concepts of Multi variable functions, vector valued functions, vector field and their limits, continuity, partial derivatives and directional derivatives. 2. Calculate the gradients, curl, divergence and volume of solids. 3. Apply change of Variables for Multiple Integrals (double and triple integrals). 4. Solve problems involving line integrals and surface integrals. 5. Use the Stokes’ theory and Divergence’s theory to simplify calculation of integral. |
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| Textbook | 1. Calculus, Ron Larson, Bruce Edwards. 2. Vector Calculus, Marsden. | |||||||||
| Additional Literature |
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| Learning Outcomes | After successful completion of the course, the student will be able to: | |||||||||
| Teaching Methods | Class lectures with lots of examples. Active tutorial sessions for engaged learning and continuous feedback on progress. Homework with more challenging or theoretical assignments. | |||||||||
| Teaching Method Delivery | Face-to-face | Teaching Method Delivery Notes | ||||||||
| WEEK | TOPIC | REFERENCE | ||||||||
| Week 1 | The inner products, length, distances, matrices, determinants and the cross products. | |||||||||
| Week 2 | The geometry of real-valued functions. Limits and continuity. | |||||||||
| Week 3 | Differentiation. Introduction to path and curves. | |||||||||
| Week 4 | Properties of the derivatives. Gradients and directional derivatives. | |||||||||
| Week 5 | Maxima and minima in several variables. | |||||||||
| Week 6 | Vector valued functions. Arc length. Vector fields. Divergence and Curl. | |||||||||
| Week 7 | Double integrals over a rectangles. The double integrals over more general region. | |||||||||
| Week 8 | Changing the order of integration. Change of variables ( polar coordinates) | |||||||||
| Week 9 | Triple integrals. Change of variables(cylindrical coordinates)(Midterm Exam) | |||||||||
| Week 10 | Change of variables (spherical coordinate). | |||||||||
| Week 11 | Line Integrals. | |||||||||
| Week 12 | Conservative Vector Fields and Independence of Path. | |||||||||
| Week 13 | surface integrals. | |||||||||
| Week 14 | Stokes theorem and Gauss' theorem. | |||||||||
| Week 15 | Review | |||||||||
| Assessment Methods and Criteria | Evaluation Tool | Quantity | Weight | Alignment with LOs |
| Final Exam | 1 | 40 | ||
| Semester Evaluation Components | ||||
| Midterm Exam | 1 | 30 | ||
| Quizzes | 3 | 30 | ||
| *** ECTS Credit Calculation *** | ||||
| Activity | Hours | Weeks | Student Workload Hours | Activity | Hours | Weeks | Student Workload Hours | |||
| Lecture Hours | 3 | 14 | 42 | Active Tutorials | 2 | 14 | 28 | |||
| Midterm Exam Study | 12 | 1 | 12 | Quizzes | 3 | 3 | 9 | |||
| Assignments | 1 | 1 | 1 | Home Study | 3 | 14 | 42 | |||
| Final Exam Study | 16 | 1 | 16 | |||||||
| Total Workload Hours = | 150 | |||||||||
| *T= Teaching, P= Practice | ECTS Credit = | 6 | ||||||||
| Course Academic Quality Assurance: Semester Student Survey | Last Update Date: 08/04/2024 | |||||||||